First thing...this ain't your Mexican Tortilla.
This is a kind of Spanish Omelet, good hot or cold. It is very popular in Spain. Over Christmas I have been reading several books written by people who have walked the Camino de Santiago de Compostella, the old medieval pilgrimage route, and almost all of them talk about eating this tasty dish for breakfast most days.
This recipe is a compilation of about 5 different ones I found, on the internet in some of my recipe books. I think it is quite authentic.
I like using a cast iron frying pan but a non stick shallow pan would work just as well.
1-3/4 cups olive oil for frying
1-3/4 lb. (about 5 medium) potatoes, such as Yukon Gold, peeled
2-1/4 tsp. coarse salt
12 to 14 oz. onions (2 to 3 medium), diced
5 medium cloves garlic, chopped
6 large eggs
1/8 tsp. freshly ground black pepper
Slice the potatoes thin, into about 1/8 inch rounds. Transfer to a bowl and sprinkle on 2 tsp. of the salt, tossing to distribute it well.
Heat a 10-1/2-inch cast iron frying pan on medium high. Add the oil. When the oil is very hot gently slip the potatoes into the oil with a spatula. Fry the potatoes, turning occasionally (trying not to break them) This can be tricky particularly as they are almost done. Adjust the heat so they sizzle but don't crisp or brown.
When the potatoes are tender, after 10 to 12 min., transfer them to a plate using a spatula. Use paper towel to soak up the excess oil.
Lower the heat a bit then add the onions and garlic to the pan. Fry, stirring occasionally. Cook, until the onions are very soft and translucent but not browned, about 7 to 9 min. Remove the pan from the heat and transfer the onions and garlic to the plate with the potatoes. Drain most of the oil from the skillet, reserving at least 1 Tbs. Wipe out the pan with a paper towel so it's clean. Scrape out any stuck-on bits, if necessary.
By now you have beaten the eggs In a large bowl with 1/4 tsp. salt, and the pepper. Add the drained potatoes, onions, and garlic and mix gently to combine with the egg, trying not to break the potatoes.
Re-heat the skillet on medium high. Add the 1 Tbs. reserved oil. Let the pan and oil get quite hot (important so the eggs don't stick), and then pour in the potato and egg mixture, spreading it evenly. Cook for 1 min. and then lower the heat to medium low, cooking until the eggs are completely set at the edges, halfway set in the center, and the tortilla easily slips around in the pan when you give it a shake, 8 to 10 min. You may need to nudge the tortilla loose with a knife or spatula.
Set a flat, rimless plate that's at least as wide as the skillet upside down over the pan. Lift the skillet off the burner and, with one hand against the plate and the other holding the skillet's handle, invert the skillet so the tortilla lands on the plate (it should fall right out).
Set the pan back on the heat and slide the tortilla into it, using the spatula to push any stray potatoes back in under the eggs as the tortilla slides off the plate. Once the tortilla is back in the pan, tuck the edges in and under itself. Cook until a fork inserted into the center comes out clean, hot, and with no uncooked egg on it, perhaps another 5 to 6 min.
Transfer the tortilla to a serving platter and let cool a few minutes. Serve
Can be eaten cold the next day.